Assertion (A): 1000 is not a perfect square. Reason (R): A perfect square must have an even number of zeros at the end. Which is correct?

Class 8Squares and Square RootsSquares and Roots

ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true but R is false
DA is false but R is true

Step-by-Step Solution

1000 ends in three zeros (odd count), so it is not a perfect square — A is true. A perfect square indeed must end in an even number of zeros — R is true and correctly explains A.

Answer: A) Both A and R are true, and R is the correct explanation of A

Key idea: Properties of perfect squares

Useful patterns to spot a perfect square (and reject non-squares):

- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square

(1 0^{2})

; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … +

(2 n - 1) = n^{2}

. Try it:

1 + 3 + 5 = 9 = 3^{2}

.

These let you reject many candidates without doing any heavy work.

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